I started keeping meticulous financial records when I went back to university several years ago (including all non-cash spending exactly, and cash spending rounded to the dollar). A quick report dumped from that time range shows my annual "mandatory" expenses during that period amounted to approximately $13,000 annually.
The report covers all of the categories I would consider as making up my baseline standard of living--the same report I use now to evaluate how long I would expect my savings to last in the event I were to become unemployed (have to be vigilant in this economy).
1) Located in the mid-western US.
2) Single, with own apartment.
3) Broadband internet, prepaid cell, VOIP "landline".
4) High-deductible/HSA individual health insurance (was working on contract at the time). I don't believe those sorts of plans are legal any more, but for someone young and healthy they were an excellent way to save while still having financial protection in a true emergency.
5) Attend a satellite campus or online classes at a public university to reduce tuition expenses. For most jobs, your degree won't matter anyway once you've gotten some experience in your field, so there's little sense for most people to blow tens of thousands of dollars on it.
6) I did not own a credit card during this time, and carried only student debt (because the interest was subsidized and I could invest that amount in something that bore interest TO me instead). That debt was paid in full within a couple of months of finding in-field employment, as soon as I was able to do so while maintaining a minimum level of savings in reserve.
Probably the only significant mitigating factor was that I mostly paid off the cheap used car I had at the time prior to returning to university. However, at $3000 in full that would still have left my annual expenses under $14000 annually if it were paid later. With the savings I set aside during that time, I purchased a low-mileage two-year old car in cash shortly before graduation (which I continue to drive to this day).
The two biggest factors, in my opinion:
1) Location. Don't expect to live in a high-cost area on a minimum wage job. If you're flexible about where you live (state-wise, not just 'what part of town'), it becomes a lot more practical to live on the cheap.
2) Discipline. If you want to live on the cheap, you need to learn how to manage money and plan ahead (months or years out--a paycheck or two out doesn't cut it). If you want a luxury/entertainment item, earn it first, then you can have it (not having credit cards helps with that). If you're single, stay that way--babies aren't cheap, but they don't make themselves.